Question 1041255
two numbers are in ratio 4:5. 
<pre><b>
Let x = the smaller number
Let y = the larger number

{{{x/y}}}{{{""=""}}}{{{4/5}}}

Cross-multiply:

{{{5x}}}{{{""=""}}}{{{4y}}}

{{{x}}}{{{""=""}}}{{{4y/5}}}
</pre></b>
if difference of their cubes is 61,
<pre><b>
{{{y^3-x^3}}}{{{""=""}}}{{{61}}}

Substitute {{{4y/5}}} for x:

{{{y^3-(4y/5)^3}}}{{{""=""}}}{{{61}}}

{{{y^3-64y^3/5^3}}}{{{""=""}}}{{{61*5^3}}}

Multiply through by 125

{{{125y^3-64y^3}}}{{{""=""}}}{{{61*5^3}}}

{{{61y^3}}}{{{""=""}}}{{{61*5^3}}}

Divide both sides by 61.

{{{y^3}}}{{{""=""}}}{{{5^3}}}

Take cube roots of both sides:

{{{y}}}{{{""=""}}}{{{5}}}

Since y = the larger number, the larger number is 5

Since x = the smaller number, and {{{x}}}{{{""=""}}}{{{4y/5}}}

the smaller number {{{""=""}}}{{{4(5)/5}}}{{{""=""}}}{{{4}}}

Edwin</pre>